area
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What is Area?
Area is defined as the amount of space covered by a 2-dimensional bounded figure. Different formulae have been derived to calculate the areas of common shapes. Surface area is a term used to describe the area covered by the surface of a 3-dimensional figure, such as a cylinder or a cube. As such, the area of any bounded surface can be calculated by using the basic formulae. Area has units of distance squared, and the SI unit is the square meter (m^{2}).
Usually, area is calculated to determine the amount of material required to cover a certain region. For example, the amount of paint required to coat a wall completely, or the size of carpet required to cover a floor.
Area of Squares and Rectangles
The area A of a square with s as the side length is equal to s x s or s2. More generally, the area of a rectangle is equal to length x width. Another quantity that needs to be introduced here is the perimeter of a rectangle, which is equal to the sum of all its sides. Note that given a number of rectangles, the perimeter of each of which is the same, they might have different areas. So, area is the measure of total space inside a shape regardless of its perimeter.
By using these basic formulae, we can calculate the area of almost any shape by dividing it into rectangles and then adding the respective areas of each individual shape.
Area of a Circle
To find the area of a circle, the square of the radius is multiplied by pi (π). Breaking up a circle into little pieces and then rearranging those pieces to form a rectangle helps us to derive this formula. We know that the circumference of a circle is given by 2πr (where ‘r’ is the radius). When we divide the circle into infinitesimally small parts, half of this distance appears at the top and the other half at the bottom. Similarly, the radius of the circle makes up the sides of that rectangle. By using the simple formula for finding the area of a rectangle, we can derive the formula for finding the area of a circle, which is length x width or πr x r = πr2.
Another Way of Finding Area
We can also find the area of a rectangle by drawing a grid of lines inside the rectangle such that it becomes tiled with squares of unit area. We can then find the area of this rectangle by counting the number of squares it contains. This method can be used to find the area of almost any shape, no matter how irregular it is. Some of the squares will be completely covered by the figure, while others, which are partially covered, can be added together to get an approximate value of area. Any arbitrary degree of accuracy can be achieved by making the squares sufficiently small.